Question

4. (12 pts) For an electron in the 4d state of hydrogen (d → e-2): a) calculate energy of the atom b) calculate the orbital angular momentum c) list the possible values of the magnetic quantum number d) for 3 values of the magnetic quantum number calculate the angle the angular momentum vector makes with the z axis.

Answer 1

Here 4 d state of hydrogen n = 4 d rightarrow l = 2. (a) E_n = -13.6/n^2 e V E_4 = -13.6/4^2 e V = -0.85 e V (b) L = squareroot l (l + 1) planckconstantovertwopi L = squareroot 2 (2 + 1) planckconstantovertwopi = squareroot 6 planckconstantovertwopi L = 2.6 times 10^-34 J . s (c) l = 2 m_l can be -l to + l m_l = -2, -1, 0, 1, 22 (d) cos theta = m_l/squareroot l (l + 1) For m_l = 2 cos theta = 2/ squareroot 6 rightdoublearrow theta = cos^-1 (2/ squareroot 6) = 35.26 degree For m_l = 1 cos theta = 1/ squareroot 6 rightdoublearrow theta = cos^-1 (1/ squareroot 6) = 65.90 degree For m_l = 0 cos theta = 0 rightdoublearrow theta = 90 degree